R. F. POLISHCHUK. “PHYSICS AND METAPHYSICS OF SPACE-TIME”. With the development of physics, the status of physical being is changing as well. The quantum-mechanical uncertainty principle makes one assume that the dimension of quantum space-time is smaller than four. One can construct physical four-dimensional space-time from light times. The macroscopic space-time emerges as an effect of dynamical quantum space-time of smaller dimension. Using dimensionless Planckian units, it is possible to connect the space-time characteristics with topology of large numbers and to reduce the metric to discrete topology (R.F. Polishchuk, "Physics and Metaphysics of Space-Time". In: Proceedings of the International Conference "Geometrization of Physics", Kazan, 1994, p. 255-258).

I. V. VOLOVICH. “PHYSICS ON THE PLANCK SCALE AND NON-ARCHIMEDEAN GEOMETRY”. In modern natural science, the space-time coordinates are represented by real numbers. Such a representation corresponds to Archimedean geometry. However, on small (Planck) scale metric fluctuations take place and the space-time geometry becomes non-Archimedean. An analytic description of such a geometry is realised with the aid of p-adic numbers. In the recent years, p-adic analysis has acquired wide application in quantum string theory, in quantum gravity, in spin glass theory and in models of memory. The theory of p-adic numbers especially strongly affects the structure of time at Planck and cosmological distances. The lecture presents an introduction to the theory of p-adic numbers and its applications (V.S. Vladimirov, I.V. Volovich and E.I. Zelenov, "P-adic Analysis and Mathematical Physics", Moscow, Fizmatlit, 1994).

A. V. KOGANOV. “INDUCTOR SPACES AS A GENERALIZING MODEL OF TIME”. The lecture presents information on the evolution of time models in modern science. The notion of an inductor space occupies a logical niche between the notions of a directed graph and that of a topological space. It enables one to build models of time for processes of different nature and to generalise the notions of an automaton and a differential equation. It has been proved that an arbitrary group of transformations can be interpreted as a group of automorphisms of a certain inductor space and therewith the group topology will be preserved. This enables one to build space-time models corresponding to processes in physics, biology and engineering (A.V. Koganov, "Inductor Spaces and Processes", Dokl. Akad. Nauk, 1992, v.324, No.5, p.953-958; A.V. Koganov, "Representation of Groups by Automorphisms of Inductor Spaces", in: Abstracts Int. Conf. "Algebra and Analysis", Kazan, 1994; A.V. Koganov, The Truth Splitting Method in Paradox Protection of Logic", in: Abstracts Int. Conf. "Logic, Methodology and Philosophy of Science", Moscow-Obninsk, 1995).

V. V. ARISTOV. “MODERN PROBLEMS OF SPACE-TIME IN PHYSICAL THEORIES AND THE MODEL APPROACH”. The program of Relativity Theory. Two branches of physical theory (special and general relativity versus statistical and quantum theory) which should have led to a synthesis in a unified field theory. Solved and unsolved problems. Geometrization of physics. The creative essence of mathematics in physics and the neo-Pythagorean ideas (Einstein, Eddington, Dirac). The meaning of the model approach. Geometrization of time. The notion of a time instant defined in terms of the configuration space of a system of particles. Metrization and a mathematical model of a clock, leading to dynamic equations. The problem of reducing the number of independent physical dimensions by building models of clocks and rulers. The possibility of dimensionless equations in physics. Development of a model for the effects of general relativity and quantum mechanics. Particle theory as an alternative to field theory. The notion of a time instant, compatible with thermodynamic quantities depending on system state. Introduction of irreversible model time connected with a distinction between two states of a system (V.V. Aristov. "Mach's Principle and a Statistical Model of Space-Time". In: Abstracts of the 8th Russian Gravitational Conference, Moscow, 1993; V.V. Aristov, "A Statistical Model of Clocks in Physical Theory", Dokl. AN, 1994, v.334, p. 161-164).

Yu. L. KLIMONTOVICH. “PHYSICS OF OPEN SYSTEMS”. Owing to matter, energy and information exchange with ambient bodies, open systems exhibit, along with degradation, self-organisation processes. Statistical criteria of self-organisation are considered. For both passive and active macroscopic system, a possibility of a unified description of kinetic, hydrodynamical and diffusion processes is demonstrated. Suggested is a statistical description of quantum macroscopic open systems, making it possible to obtain answers to the "eternal" questions: is the quantum-mechanical description full? Are there hidden parameters in quantum theory? (Yu.L. Klimontovich, "Statistical Theory of Open Systems", Moscow, Yanus, 1995.)

V. P. MAIKOV. “TIME, ORDER, MACROQUANTA AND EINSTEIN'S PROGRAM OF THE DEVELOPMENT OF PHYSICS”. The report considers the results of generalising the well-known phenomenon of macroquantum effects to an independent extended version of classical equilibrium thermodynamics. The methodological and physical bases of the generalisation are: the macroscopic (but not statistical) phenomenology of equilibrium thermodynamics; macroquantization; nonlocality; the relativism of general relativity; usage of only first principles of physics. A formal base for describing macroscopically elementary phenomena is the use of physically extremely small quantities instead of differential operators. For this purpose the well-known uncertainty relations are used. They make it possible to introduce the characteristic space and time scales to the description of a thermodynamical equilibrium without addressing to the quantum-mechanical procedures. The above scales determine the properties of the space-time metric in the Einstein understanding. In the equilibrium theory under consideration, unlike the non-equilibrium one (I. Prigogine), the time irreversibility phenomenon is connected with the order (entropy reduction) and the macroquanta of the space-time metric (V.P. Maikov, "Phenomenological theory of an equilibrium isotropic material medium (the quantum-thermodynamic approach)", in: Reports of Internat. Research and Engineering Conference "Urgent Problems of Basic Research", v.3: Section of Theoretical and Experimental Physics, Moscow, MGTU, 1991, p. 106-109).

(1) Yu. A. DANILOV.“THE "ARROW OF TIME" AFTER THE PUBLICATION OF THE BOOK "TIME, CHAOS, QUANTA" BY I. PRIGOGINE AND I. STENGERS”. The irreversibility emerges on a fundamental level rather than due to averaging the reversible equations of motion.